Asymptotically holomorphic embeddings of presymplectic manifolds

Abstract

We apply Donaldson-Auroux's asymptotically holomorphic methods to construct asymptotically holomorphic embeddings of presymplectic closed manifolds of constant rank with integral form into Grassmannians $\text{Gr}(r,N)$. In particular, we obtain asymptotically holomorphic embeddings into the projective spaces $C{\text{P}}^{N-1}$ such that the pull-back of the Fubini-Study form is cohomologous to $k\omega /2\pi$ for large integers $k$. Moreover, we can construct asymptotically holomorphic immersions along the symplectic distribution of presymplectic manifolds into the projective spaces.